Testing local/global rigidity is known to be a hard problem even if a tensegrity is a bar-joint framework.
The situation is even worse for tensegrities since a generic assumption for point configurations does not seem as powerful as the ordinary bar-joint case, see, e.g. [1]}, [2]}.
Hence, the standard approach in practice is to check a sufficient condition. Commonly used sufficient conditions for rigidity are infinitesimal rigidity [3]}, prestress stability [4]}, and super stability [5]}.
